Fetching the paper…
Reading the bibliography…
A class of models of long waves in dispersive media with coupled quadratic nonlinearities on a periodic domain $\mathbb{T}$ are studied.
1907
Earlier work this paper cites.
M. Slemrod, A note on complete controllability and stabilizability for linear control systems in Hilbert space, SIAM J. Control. 12 (1974) 500–508
1974
Earlier work this paper cites.
R. M. Miura, The Korteweg-de Vries equation: A survey of results, SIAM Rev. 18 (1976) 412–-459
1976
Earlier work this paper cites.
D. Russell, Controllability and Stabilizabilization Theory for Linear Partial Differential Equations: Recent Progress and Open Questions, SIAM Review. 20 (1978) 639–739
1978
Earlier work this paper cites.
R. Hirota, J. Satsuma. Soliton solutions of a coupled Korteweg-de Vries equation. Phys. Lett. A. 85(8-9) (1981) 407–408
1981
Earlier work this paper cites.
T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equations, Advances in Mathematics Supplementary Studies, Academic Press, New York, 93–128 (1983)
1983
Earlier work this paper cites.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied mathematical sciences. Springer, (1983)
1983
Earlier work this paper cites.
J. A. Gear, R. Grimshaw, Weak and strong interactions between internal solitary waves, Stud. Appl. Math. 70 (1984) 235–-258
1984
Earlier work this paper cites.
J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part II: The KdV equation, Geom. & Funct. Anal. 3 (1993) 209–262
1993
Earlier work this paper cites.
D. Russell, B.-Y. Zhang, Controllability and stabilizability of the third order linear dispersion equation on a periodic domain. SIAM J. Cont. Optim. 31 (1993) 659–676
1993
Earlier work this paper cites.
C. E. Kenig, G. Ponce, L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc. 9, (1996) 573–603
1996
Earlier work this paper cites.
D. Russell, B.-Y. Zhang, Exact contollability and stabilizability of the Korteweg-De Vries equation, Transactions of the American Mathematical Society. 348 9 (1996) 3643–3672
1996
Earlier work this paper cites.
L. Rosier, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain, ESAIM Control Optim. Cal. Var. 2 (1997) 33–55
1997
Earlier work this paper cites.
B.-Y. Zhang, Exact boundary controllability of the Korteweg-de Vries equation, SIAM J. Cont. Optim. 37 (1999) 543–565
1999
Cited alongside, same era.
J. L. Bona, S.-M Sun, B.-Y. Zhang, The initial-boundary value problem for the Korteweg- de Vries equation in a quarter plane, Trans. American Math. Soc. 354 (2001) 427–490
2001
Cited alongside, same era.
J. J. Bona, M. Chen, J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I. Derivation and linear theory, J. Nonlinear Sci. 12 (2002) 283–318
2002
Cited alongside, same era.
A. Gruünrock, New applications of the Fourier restriction norm method to wellposedness problems for nonlinear evolution equations. Doctoral Thesis. Bergischen University. (2002)
2002
Cited alongside, same era.
A. J. Majda, J. A. Biello, The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves, J. Atmospheric Sci. 60 (15) (2003)1809–1821
C. Laurent, L. Rosier, B.-Y. Zhang, Control and stabilization of the Korteweg-de Vries equation on a periodic domain, Communications in Partial Differential Equations. 35 (2010), 707–744
2010
Later among the works it cites.
J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Sharp global well-posedness for KdV and modified KdV on R and T, Computer Physics Communication. 184 (2013) 812–823
2013
Later among the works it cites.
J. L. Bona, J. Cohen, G. Wang, Global well-posedness of a system of KdV-type with coupled quadratic nonlinearities, Nagoya Math. J. 215 (2014) 67-–149
2014
Later among the works it cites.
R. A. Capistrano-Filho, A. F. Pazoto, L. Rosier, Internal controllability for the Korteweg-de Vries equation on a bounded domain, ESAIM Control Optimization and Calculus Variations. 21 (2015) 1076-1107
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2003
Cited alongside, same era.
V. Komornik, P. Loreti, Fourier Series in Control Theory. Springer Verlag. 2005
2005
Cited alongside, same era.
F. Linares, J. Ortega, On the controllability and stabilization of the linearized Benjamin-Ono equation, ESAIM Control Optim. Calc. Var. 11 (2005) 204–218
2005
Cited alongside, same era.
B. Dehman, P. Gérard, G. Lebeau, Stabilization and control for the nonlinear Schrödinger equation on a compact surface, Math. Z. 254, (2006) 729–-749
2006
Cited alongside, same era.
T. Tao, Nonlinear Dispersive Equations, Local and Global Analysis. CBMS Regional Conference Series in Mathematics, 106. Providence, RI: American Mathematical Society (2006)
2006
Cited alongside, same era.
E. Cerpa, Exact controllability of a nonlinear Korteweg-de Vries equation on a critical spatial domain, SIAM J. Control Optim. 43 (2007) 877–-899
2007
Cited alongside, same era.
S. Micu, J.H. Ortega, L. Rosier, B.-Y. Zhang, Control and stabilization of a family of Boussinesq systems, Discrete Contin. Dyn. Syst. 24 (2009) 273–-313
2009
Cited alongside, same era.
T. Oh, Diophantine conditions in well-posedness theory of coupled KdV-type systems: Local theory, Int. Math. Res. Not. IMRN, 18 (2009), 3516–3556
2009
Cited alongside, same era.
C. Laurent, F. Linares, L. Rosier, Control and Stabilization of the Benjamin-Ono Equation in L 2 ( 𝕋 ) L^{2}(\mathbb{T}) , Arch Rational Mech. Anal. 218 (2015) 1531–1575
2015
Later among the works it cites.
F. Linares, L. Rosier, Control and stabilization of the Benjamin-Ono equation on a periodic domain, Transactions of the american mathematical society. 7 367 (2015) 4595–4626
2015
Later among the works it cites.
X. Zhao, B.-Y. Zhang, Global controllability and stabilizability of Kawahara equation on a periodic domain, Math. Control Related Fields. 5 (2) (2015) 335–-358
2015
Later among the works it cites.
R. A. Capistrano-Filho, S.-M. Sun, B.-Y. Zhang, Initial boundary value problem for Korteweg-de Vries equation: a review and open problems, São Paulo Journal of Mathematical Sciences. 13 (2019) 402–417
2019
Later among the works it cites.
R. de A. Capistrano-Filho, V. Komornik, A. Pazoto, Pointwise control of the linearized Gear-Grimshaw system, Evolution Equations & Control Theory. 9 3 (2020) 693–719
2020
Later among the works it cites.
J. R. Quintero, A. M. Montes, On the exact controllability and the stabilization for the Benney-Luke equation, Mathematical Control & Related Fields. 10:2 (2020) 275–304
2020
Later among the works it cites.
M. Panthee, F. Vielma Leal, On the controllability and stabilization of the Benjamin equation on a periodic domain, to apper Annales de l’Institut Henri Poincaré C, Analyse non linéaire (2020)
2020
Later among the works it cites.
R. A. Capistrano-Filho, Weak damping for the Korteweg-de Vries equation, Electron. J. Qual. Theory Differ. Equ. No. 43 (2021), 1-25
2021
Closest in time.
R. A. Capistrano-Filho and M. Cavalcante, Stabilization and control for the biharmonic Schrödinger equation, Appl Math Optim 84 (2021), 103-144
2021
Closest in time.